9-9 할리데이 11판 솔루션 일반물리학

$$\put\begin{cases} i:\text{Start}\\ j:\text{After A B Crash}\\ k:\text{After Wall Crash}\\ \end{cases}$$ $$\begin{cases} m_1&=6.6\ut{kg}\\ v_{1k}&=v_{1j}\\ v_{2k}&=-v_{2j}\\ v_{1k}&=v_{2k}=v_k\\ \end{cases}$$ $$\text{Elastic Collision}\Harr\vec v_{\text{in}}+ \vec v_{\text{out}}=0,$$ $$\begin{aligned} v_{1i}+v_{1j}&=v_{2i}+v_{2j}\\ 0+v_{1k}&=v_{2i}-v_{2k}\\ v_{k}&=v_{2i}-v_{k}\\ v_{2i}&=2v_k \end{aligned}$$ $$\Delta \Sigma \vec P=0,$$ $$\begin{aligned} m_2v_{2i}&=m_1v_{1j}+m_2v_{2j}\\ m_2(2v_k)&=m_1v_k-m_2v_k\\ 3m_2v_k&=m_1v_k\\ \end{aligned}$$ $$\begin{aligned} m_2&=\frac{1}{3}m_1\\ &=\frac{11}{5}\ut{kg}\\ &=2.2\ut{kg} \end{aligned}$$